A284798 - OEIS

%I #17 Nov 04 2023 14:34:55

%S 1,4,6,13,21,34,40,46,60,66,72,97,121,145,177,201,225,268,286,304,346,

%T 364,382,424,442,460,510,528,546,588,606,624,666,684,702,781,853,925,

%U 1021,1093,1165,1261,1333,1405,1509,1581,1653,1749,1821,1893,1989,2061,2133

%N Antipalindromic numbers in base 3.

%C Fixed points of the transform A284797.

%C A b-adic "antipalindrome" is a string of digits x where the application of the map d -> b-1-d to each digit, followed by reversal of all digits, is equal to x.  This sequence lists the integers whose base-3 representation (with no leading zeros) has this property.

%H Lubomira Dvorakova, Stanislav Kruml, and David Ryzak, <a href="https://arxiv.org/abs/2008.06864">Antipalindromic numbers</a>, arXiv preprint arXiv:2008.06864 [math.CO], August 16 2020.

%e 34 is a term of the sequence because 34 in base 3 is 1021, its digit-by-digit complement in base 3 is 1201 and the digit reverse is again 1021.

%p P:=proc(q,h) local a,b,k,n; for n from 1 to q do a:=convert(n,base,h); b:=0;

%p for k from 1 to nops(a) do a[k]:=h-1-a[k]; b:=h*b+a[k]; od; if b=n then print(n); fi; od; end: P(10^2,8);

%o (Python)

%o from itertools import count, islice

%o from gmpy2 import digits

%o def A284798_gen(): return (n for n in count(0) if not n+int((s:=digits(n,3)[::-1]),3)+1-3**len(s))

%o A284798_list = list(islice(A284798_gen(),35)) # _Chai Wah Wu_, Feb 04 2022

%Y Cf. A035928, A284797.

%K nonn,base,easy

%O 1,2

%A _Paolo P. Lava_, Apr 03 2017

%E New name from _Jeffrey Shallit_, Nov 04 2023